The fractional tajimi-kanai model of earthquake gound motion

Abstract

This paper introduces a Fractional Tajimi-Kanai (TK) filter. The term Cgx̊g of the classicalTK is substituted by C̄g (CDβ0+x g)(t) that is the Caputo fractional derivatives where C̄g and β(0≤β≤1) are parameter depending on the soil deposit. The main advantage of this new model with respect to the classical one is that the variance of the rate of acceleration remain finite. This means that the mean number of zero crossing, first passage and other relevant statistics may be evaluated. Moreover it is shown that such a new model is a multiscale one and then it may account for the complex behaviour of the ground at hands.